Zyalura and Satcomer are right. A couple of replacements needed, despite strat saying "any" breed will work. SS Brown Rabbit in place of Noblegarden Bunny (which I don't have), BB Rapana Whelk instead of SS, and Scooter did not have much work left to do.

I couldn't kill Lilly with any of the rabbits I have so used a Pygmy Cow. Stampede and Udder Destruction works every time. However the snails still proved troublesome as well but after a few tries with bad RNG I finally got it along with my Family Battler achieve!

Use S/S rabbit, and use nether roach 1,x,x as third pet, nether roach spam nether blast, it is still a bit of RNG depends if ticker is faster than rapana whelk, as ticker without flying speed buff is same speed as rapana